Abstract.
We consider a general model of discrete-time random walk X t on the lattice ν, ν = 1,..., in a random environment ξ={ξ(t,x):(t,x)∈ ν+1} with i.i.d. components ξ(t,x). Previous results on the a.s. validity of the Central Limit Theorem for the quenched model required a small stochasticity condition. In this paper we show that the result holds provided only that an obvious non-degeneracy condition is met. The proof is based on the analysis of a suitable generating function, which allows to estimate L 2 norms by contour integrals.
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Partially supported by C.N.R. (G.N.F.M.) and M.U.R.S.T. research funds.
Partially supported by C.N.R. (G.N.F.M.) and M.U.R.S.T. research funds, by R.F.F.I. grants n. 99-01-00284, 97-01-00714, and CRDF research funds N RM1-2085.
Partially supported by C.N.R. (G.N.F.M.) and M.U.R.S.T. research funds.
Mathematics Subject Classification (2000): 60J15, 60F05, 60G60, 82B41
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Boldrighini, C., Minlos, R. & Pellegrinotti, A. Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive. Probab. Theory Relat. Fields 129, 133–156 (2004). https://doi.org/10.1007/s00440-003-0331-x
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DOI: https://doi.org/10.1007/s00440-003-0331-x